Breakdown of kaze ga tuyoi desu kara, doa wo simete mo ii desu ka?

Questions & Answers about kaze ga tuyoi desu kara, doa wo simete mo ii desu ka?
Yes. Since 強い is an い-adjective, you can attach から directly to its dictionary form:
風が強いからドアを閉めてもいいですか?
This still sounds polite because of いいですか. However, keeping 強いですから makes both clauses uniformly polite.
Absolutely. ので often sounds softer or more formal than から. You’d say:
風が強いのでドアを閉めてもいいですか?
Both から and ので work to express “because.”
The dictionary (plain) form is 閉める. To make the te-form for ru-verbs, drop る and add て:
閉める → 閉めて
~てもいいですか means “May I ~?” or “Is it okay if I ~?” Construction:
1) Verb in te-form (e.g. 閉めて)
2) も (“even if”)
3) いいですか (“is it okay?”)
いい is an い-adjective meaning “good.” Adding です makes the question polite:
いい → いいです
Then いいですか turns it into “is it okay?”
You can drop most politeness markers:
風が強いからドア閉めていい?
Or even shorter:
風強いし、ドア閉めていい?
Both ask permission.
- 閉めてもいいですか sounds natural and polite.
- 閉めてもかまいませんか is slightly more formal/indirect (“would you mind if I…?”). The nuance is very close, but かまいません literally means “it won’t bother you.”